Answer
$x \gt \frac{c-b}{a}$
The solution set is $~~~(\frac{c-b}{a},\infty)$
Work Step by Step
Note that $a$, $b$, and $c$ are negative constants.
$ax+b \lt c$
$ax \lt c-b$
$x \gt \frac{c-b}{a}$
The solution set is $~~~(\frac{c-b}{a},\infty)$
Note that the inequality changes from $~~\lt~~$ to $~~\gt~~$ when we divide by $a$ because $a \lt 0$